Applying a new dispersion model to turbulent premixed flames

Transcription

1 Applying a new dispersion model to turbulent premixed flames Federico Ghirelli Fifth OpenFOAM Workshop Gothenburg, June 2010

2 Point source in steady homogeneous turbulence Fundamental experiment: In a statistically stationary and homogeneously turbulent flow the fluid in position X0 is marked with a tracer at time t0. Several realizations give the ensemble average tracer concentration field. The dispersion of the tracer is characterised by the standard deviation σ(t) of the concentration.

3 Point source in steady homogeneous turbulence Due to velocity correlation [1], σ develops as t at the early stage and as t 1/2 later on. The turbulent diffusivity is not stationary (!)

4 Point source in steady homogeneous turbulence If you are using a RANS model implemented in a general purpose CFD package, then YOU ARE MODELLING DISPERSION THIS WAY!!! i.e. as if turbulent diffusivity were stationary.

5 The TFC and FSC models TFC model [4] FSC model [2][3] does not account for velocity correlation accounts for velocity correlation usually applied to stabilized flames usually applied to spark ignited flames implemented in general purpose CFD Dt,t and Ut,t are explicit functions of time (or position) not implemented in general purpose CFD

6 Aim of the work Formulation of a model that fulfills the following requirements: 1. Same set of equations for both spark ignited flames and stabilized (steady) flames 2. No parameters depending explicitly on time or position 3. Accounts for velocity correlation

7 Eulerian dispersion model (Edimo) Uses two transport equations (one for the transported scalar C and one for its turbulent diffusivity Dc) No parameters dependent on time or position Accounts for velocity correlation [5] Point source in steady homogeneous turbulence

8 Applying Edimo to premixed flames Main modelling step: Reformulation of the chemical source term of the FSC model without explicit dependence on time (in terms of Dc). The resulting flame model satisfies the requirements 1., 2. and 3. above.

9 Flame model validation 1 (V flame) Measured [6] and computed progress variable contours at C=0.1, 0.5, 0.9

10 Model validation 2 (Volvo burner) Symbols: measured [7] temperature Solid line: present model Dashed line: TFC model Sections at 0.15, 0.35 and 0.55 m from the flame holder

11 Model validation 3 (Moreau burner) Measured [8] and computed temperatures at two sections downstream of the inlet.

12 Premixed flame model test According to [2][9] premixed flame models can be tested in 1D (planar flame) and should predict: Self similar flame profiles Universally observed flame profile Flame thickness growth according to turbulent diffusion law Flame speed should grow at a qualitatively different rate than flame thickness growth

13 Flame model test results Fig 1: normalized progress variable profiles: Solid lines are computed at t/ τ=0.5, 2, 5 and Da=1, 1000 (all curves collapse on a single line). Dashed line: empirical profile [2] Fig 2: Flame thickness development Fig 3: Flame speed growth compared to thickness growth

14 Conclusions The proposed model: Accounts for velocity correlation Uses a single set of equations for spark ignited and stabilized flames It does not include parameters depending on time or position It performs better than the TFC model It satisfies fully the premixed flame model test fullfills all the goals of the original project (and more)

15 Discussion When modelling dispersion with default Eulerian models, it is necessary to calibrate ScT. Recommended values vary from 0.2 to 1.3 [10] (usually 0.7 in premixed flame apps.) In the present study, ScT was set to 1 and did not require calibration. Is ScT needed because velocity correlation is neglected? Can Edimo replace ScT calibration?

16 References [1] G.I. Taylor, Diffusion by continuous movements, Proc. Lond. Math. Soc. 20 (1921) 196 [2] A.N. Lipatnikov and J. Chomiak, Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi dimensional simulations. Prog. Energy Comb. Sci. 28 (2002) 1 74 [3] A.N. Lipatnikov and J. Chomiak, A simple model of unsteady turbulent flame propagation, SAE transactions. J Engines 106 (1997) 2441 SAE paper [4] V.L. Zimont, Gas premixed combustion at high turbulence. Turbulent flame closure combustion model, Experimental Thermal and Fluid Science 21 (2000) [5] F. Ghirelli, Eulerian modeling of turbulent dispersion from a point source, Computers and Fluids, 38 (2009) 1795 [6] F. Dinkelacker and F. Höltzer, Investigation of a Turbulent Flame Speed Closure Approach [7] A. Sjunneson, S. Olovsson and B. Sjöblom, Validation rig a tool for flame studies, 10th International Symposium on Air Breathing Engines (ISABE) 1991, UK [8] P. Moreau, Turbulent flame development in a high velocity premixed flow, AIAA paper 1977:77/49 [9] A.N. Lipatnikov and J. Chomiak, Developing premixed turbulent flames: Part I. Self similar regime of flame propagation.combust. Sci. and Tech. 162 (2001) [10] Y. Tominaga, T. Stathopoulos, Turbulent Schmidt numbers for CFD analysis with various types of flowfield, Atmospheric Environment 41 (2007)